For now, we have txid:vout as a previous transaction output. This means that to have a stable TXID, we are forced to use SIGHASH_ALL somewhere, just to prevent any transaction modifications that can happen during adding some inputs and outputs. But it seems that new sighashes could be far more powerful than we expected: it is technically possible to not only remove previous transaction output by using SIGHASH_ANYPREVOUT. We can do more and do it better, we could decide, how to calculate this txid at all!

So, something like SIGHASH_PREVOUT_NONE would be similar to SIGHASH_NONE (applied to the previous transaction, taken from txid). To have SIGHASH_ANYPREVOUT, we need to remove absolutely everything, I don't know any such sighashes, because even SIGHASH_NONE | SIGHASH_ANYONECANPAY will commit at least to some fields, for example to the locktime. But, if we introduce SIGHASH_PREVOUT_XYZ flags for all existing sighashes, we would have this:

SIGHASH_PREVOUT_NONE
SIGHASH_PREVOUT_SINGLE
SIGHASH_PREVOUT_ALL
SIGHASH_PREVOUT_ANYONECANPAY

Then, the procedure is as follows: we use txid:vout to find our previous transaction. Then, we apply those sighashes to this previous transaction, to form a new txid, that will be checked during every OP_CHECKSIG-based opcode. In this way, our txid:vout is used just to do transaction lookup, after that, sighashes can be applied to the previous transaction, so our txid could remain stable, even if someone will add some inputs and outputs.

By default, we could use SIGHASH_PREVOUT_ALL, that would mean our txid:vout remains unchanged. Then, SIGHASH_PREVOUT_SINGLE would obviously mean, that we want to commit only to this particular previous transaction output. That would allow adding any new outputs to the previous transaction, without affecting our replaced txid, but also without blindly accepting any txid, because some data of the previous transaction would be still hashed.

Then, SIGHASH_PREVOUT_NONE is an interesting case, because it would mean that no outputs of the previous transaction are checked. But still, the inputs will be! That would mean: "I don't care about in-between addresses, but I care that it was initiated from these inputs". In this case, it is possible to choose some input without those flags, and then apply SIGHASH_PREVOUT_NONE many times, to make sure that everything started from that input, but everything in-between can be anything.

All of those three SIGHASH_PREVOUT_XYZ flags could be combined with SIGHASH_PREVOUT_ANYONECANPAY. That would mean all inputs of the previous transaction are discarded, except from the input number matching "vout". Or we could just use SIGHASH_PREVOUT_ANY instead and discard all inputs from that previous transaction, that could also be combined with other sighashes.

So, to sum up, by applying sighashes to the previous transaction, instead of allowing for any transaction, we could still have some control of our txid, and I think it could be better than just saying "give me any txid, I will accept that". I think in most cases we don't want to allow any txid: we want to only "control the flow", just to make sure that our signatures will sign what we want and will not be invalidated by changing some transaction inputs and outputs, unrelated to the currently-checked signature.
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